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A091980
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Recursive sequence; one more than maximum of products of pairs of previous terms with indices summing to current index.
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9
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1, 2, 3, 5, 7, 11, 16, 26, 36, 56, 81, 131, 183, 287, 417, 677, 937, 1457, 2107, 3407, 4759, 7463, 10843, 17603, 24373, 37913, 54838, 88688, 123892, 194300, 282310, 458330, 634350, 986390, 1426440, 2306540, 3221844, 5052452, 7340712, 11917232, 16500522
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OFFSET
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1,2
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COMMENTS
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The maximum is always obtained by taking i as the power of 2 nearest to n/2. - Anna de Mier, Mar 12 2012
a(n) is the number of (binary) max-heaps on n-1 elements from the set {0,1}. a(7) = 16: 000000, 100000, 101000, 101001, 110000, 110010, 110100, 110110, 111000, 111001, 111010, 111011, 111100, 111101, 111110, 111111. - Alois P. Heinz, Jul 09 2019
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REFERENCES
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A. de Mier and M. Noy, On the maximum number of cycles in outerplanar and series-parallel graphs, Graphs Combin., 28 (2012), 265-275.
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LINKS
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Eric Weisstein's World of Mathematics, Heap
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FORMULA
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a(n) = 1 + max_{i=1..n-1} a(i)*a(n-i) for n > 1, a(1) = 1.
a(n) = Sum_{k=0..n-1} A309049(n-1,k).
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MAPLE
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b:= proc(n) option remember; `if`(n=0, 1, (g-> (f->
1+b(f)*b(n-1-f))(min(g-1, n-g/2)))(2^ilog2(n)))
end:
a:= n-> b(n-1):
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MATHEMATICA
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a[n_] := a[n] = 1 + Max[Table[a[i] a[n-i], {i, n-1}]]; a[1] = 1;
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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